A) \[\left( 3,\text{ }\infty \right)\]
B) (1, 3/2]
C) (3/2, 2]
D) (2, 3]
Correct Answer: A
Solution :
\[si{{n}^{2}}\,\theta \,\,=\,\,co{{s}^{2}}\theta \,\,({{e}^{2}}\,-1)\] \[{{\tan }^{2}}\,\theta \,\,=\,\,{{e}^{2}}\,\,-1\] \[1\text{ }+\text{ }ta{{n}^{2}}\theta \text{ }=\text{ }{{e}^{2}}\] \[e\,\,=\,\,\sqrt{{{\sec }^{2}}\,\theta }\] \[e\,\,=\,\,sec\,\theta \] \[\sec \,\,\theta \,\,>\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,\frac{1}{\cos \,\theta }\,\,>\,\,2\] \[\theta \,\in \,\,\left( \frac{\pi }{3},\,\,\frac{\pi }{2} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,<\,\,\cos \,\theta \,\,\,<\,\,sss\,\,\frac{1}{2}\,\] length of LR \[=\,\,\frac{2{{b}^{2}}}{a}\,\,\,=\,\,\frac{2.{{\sin }^{2}}\,\theta }{\cos \,\theta }\,\,\] = \[\frac{2(1-co{{s}^{2}}\theta )}{\cos \,\theta }\] \[\,\left( \frac{\pi }{3},\,\,\,\frac{\pi }{2} \right)\,\,\uparrow \,\,function\] min exist at \[\theta \,\,\,=\,\,\frac{\pi }{3}\] max exist at \[\theta \,\,\,=\,\,\frac{\pi }{2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,(3,\,\,\,\infty )\]You need to login to perform this action.
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